Inhomogeneity reconstructions in tendon ducts via boundary integral equations

Abstract

In this study, as an alternative to the formerly presented investigations, Newton-type numerical algorithms are proposed to find location and shape of an air void inside of a tendon duct and to identify gathered metallic bars in a concrete column. The simulated structures are illuminated by four acoustic sources at a fixed frequency such that the scattered field is measured in a near-field region at 128 points. According to the nature of physical problems, the Dirichlet boundary condition is employed to model air-filled cavities and transmission conditions are assumed for metallic objects. Additionally, conductive boundary conditions are suggested for a more realistic representation of the inhomogeneities for the rusty metallic skin of the duct. Potential approaches are used to derive boundary integral equations. The proper treatment of the ill-conditioned equations is established via Tikhonov regularization. Applicability of the proposed inversion algorithms is tested with realistic parameters for different scenarios using noisy scattered field data and accurate numerical results are presented at 10 kHz for the unknown physical properties of the duct's skin.